Dungeons & Dragons coined the term "dungeon master" for the role of the player running the game and adjudicating the rules. When is "game master" first attested (as in, "proven to have existed by records") as a replacement, generic name for the same player role?

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Dungeons & Dragons did not coin the term "dungeon master." The first edition instead uses the term "referee" throughout. "Dungeon master" seems to have spread from West Coast fans back to TSR through various early fanzines, especially Alarums & Excursions. Early fans from the very dawn of D&D used the term "gamesmaster" (for example in Minneapa, as of March 1974) to refer to the referee. TSR invoked "gamesmaster" itself in the Strategic Review in its advertisements for D&D referees well before the term "dungeon master" gained currency (we see DM by the end of 1975, in for example Gygax's foreword to the Blackmoor pamphlet).

Fans knew the term "gamesmaster" already when D&D came out because it had a long pedigree in postal gaming circles. The term "gamesmaster" was in use in the postal Diplomacy community as early as 1963, in John Boardman's Graustark. Many other postal games, including the postal fantasy game Midgard, employed "gamesmaster" or "game master" and even the abbreviation "GM" well before D&D appeared on the scene. "Dungeon master" is a clear adaptation of "gamesmaster" to D&D.

The first edition of Tunnels & Trolls, incidentally, used the term "dungeon master," which Arizona fans probably picked up from APA-L (a Los Angeles precursor to Alarums & Excursions).

All of this is detailed at some length in Playing at the World (start perhaps at the top of p.492).